fix: Smooth 2d shadow view of complex multibrot

src/fractal/renderer.rs

@@ -13,7 +13,9 @@ use std::collections::HashMap;
 use std::sync::Arc;
 
 use eframe::egui_wgpu::{self, wgpu};
+use wgpu::util::DeviceExt as _;
 
+use super::kind::FractalKind;
 use super::reference::RefOrbit;
 use crate::lights::{GpuLight, Light, MAX_LIGHT_COUNT, gpu_lights};
 
@@ -159,6 +161,240 @@ fn fullscreen_pipeline(
     })
 }
 
+/// Stride between the per-pass step uniforms in [`Lipschitz::steps`]
+/// (WebGPU's minimum uniform-buffer offset alignment).
+const LIPSCHITZ_STRIDE: u32 = 256;
+/// Step uniforms held: slot k holds step 2^k, enough for any texture size.
+const LIPSCHITZ_SLOTS: u32 = 32;
+
+/// Whether the shadow / 3D view of `u` rebuilds its DE height field as a
+/// distance field (see `lipschitz.wgsl`): only Complex Multibrot, whose
+/// branch cut makes the DE jump (seams in shadow, walls in 3D). Every other
+/// kind and classic colouring keep the DE as is.
+fn wants_envelope(u: &Uniforms) -> bool {
+    let cm = FractalKind::ComplexMultibrot as u32;
+    u.rendering_mode != 0 && (u.kind == cm || (u.morph_w > 0.0 && u.morph_from == cm))
+}
+
+/// The distance-field passes (`lipschitz.wgsl`): seed, jump-flood and
+/// compose pipelines, their shared input layout (data texture, seed texture,
+/// step uniform at a dynamic offset) and the buffer of every pass's step.
+#[derive(Clone)]
+struct Lipschitz {
+    seed: wgpu::RenderPipeline,
+    jump: wgpu::RenderPipeline,
+    compose: wgpu::RenderPipeline,
+    layout: wgpu::BindGroupLayout,
+    steps: wgpu::Buffer,
+}
+
+impl Lipschitz {
+    fn new(device: &wgpu::Device) -> Self {
+        let module = device.create_shader_module(wgpu::ShaderModuleDescriptor {
+            label: Some("lipschitz"),
+            source: wgpu::ShaderSource::Wgsl(
+                concat!(
+                    include_str!("../shaders/common.wgsl"),
+                    include_str!("../shaders/lipschitz.wgsl"),
+                )
+                .into(),
+            ),
+        });
+        let texture_entry = |binding| wgpu::BindGroupLayoutEntry {
+            binding,
+            visibility: wgpu::ShaderStages::FRAGMENT,
+            ty: wgpu::BindingType::Texture {
+                sample_type: wgpu::TextureSampleType::Float { filterable: false },
+                view_dimension: wgpu::TextureViewDimension::D2,
+                multisampled: false,
+            },
+            count: None,
+        };
+        let layout = device.create_bind_group_layout(&wgpu::BindGroupLayoutDescriptor {
+            label: Some("lipschitz bind group layout"),
+            entries: &[
+                texture_entry(0),
+                texture_entry(1),
+                wgpu::BindGroupLayoutEntry {
+                    binding: 2,
+                    visibility: wgpu::ShaderStages::FRAGMENT,
+                    ty: wgpu::BindingType::Buffer {
+                        ty: wgpu::BufferBindingType::Uniform,
+                        has_dynamic_offset: true,
+                        min_binding_size: wgpu::BufferSize::new(16),
+                    },
+                    count: None,
+                },
+            ],
+        });
+        let pipeline_layout = device.create_pipeline_layout(&wgpu::PipelineLayoutDescriptor {
+            label: Some("lipschitz pipeline layout"),
+            bind_group_layouts: &[Some(&layout)],
+            immediate_size: 0,
+        });
+        let pipeline = |label, entry| {
+            fullscreen_pipeline(device, label, &module, &pipeline_layout, entry, DATA_FORMAT, &[])
+        };
+        let mut contents = vec![0u8; (LIPSCHITZ_STRIDE * LIPSCHITZ_SLOTS) as usize];
+        for k in 0..LIPSCHITZ_SLOTS {
+            let at = (k * LIPSCHITZ_STRIDE) as usize;
+            contents[at..at + 4].copy_from_slice(&(1i32 << k.min(30)).to_ne_bytes());
+        }
+        let steps = device.create_buffer_init(&wgpu::util::BufferInitDescriptor {
+            label: Some("lipschitz steps"),
+            contents: &contents,
+            usage: wgpu::BufferUsages::UNIFORM,
+        });
+        Self {
+            seed: pipeline("lipschitz seed pipeline", "fs_seed"),
+            jump: pipeline("lipschitz jump pipeline", "fs_jump"),
+            compose: pipeline("lipschitz compose pipeline", "fs_compose"),
+            layout,
+            steps,
+        }
+    }
+
+    /// A pass input reading the data texture `data` and seed texture `seeds`.
+    fn bind_group(
+        &self,
+        device: &wgpu::Device,
+        data: &wgpu::TextureView,
+        seeds: &wgpu::TextureView,
+    ) -> wgpu::BindGroup {
+        device.create_bind_group(&wgpu::BindGroupDescriptor {
+            label: Some("lipschitz bind group"),
+            layout: &self.layout,
+            entries: &[
+                wgpu::BindGroupEntry {
+                    binding: 0,
+                    resource: wgpu::BindingResource::TextureView(data),
+                },
+                wgpu::BindGroupEntry {
+                    binding: 1,
+                    resource: wgpu::BindingResource::TextureView(seeds),
+                },
+                wgpu::BindGroupEntry {
+                    binding: 2,
+                    resource: wgpu::BindingResource::Buffer(wgpu::BufferBinding {
+                        buffer: &self.steps,
+                        offset: 0,
+                        size: wgpu::BufferSize::new(16),
+                    }),
+                },
+            ],
+        })
+    }
+}
+
+/// Targets for the distance field of one data texture: two ping-pong seed
+/// textures for jump flooding, and the output (data with the rebuilt DE).
+struct Envelope {
+    /// `[seeds A, seeds B, output]`, kept so they can be `destroy()`ed with
+    /// the rest of the cache.
+    textures: [wgpu::Texture; 3],
+    views: [wgpu::TextureView; 3],
+    /// Pass inputs: the data texture with seeds A, and with seeds B.
+    inputs: [wgpu::BindGroup; 2],
+    /// Step slot of each jump pass, in order (see [`lipschitz_slots`]).
+    slots: Vec<u32>,
+}
+
+impl Envelope {
+    fn new(
+        device: &wgpu::Device,
+        lp: &Lipschitz,
+        data: &wgpu::TextureView,
+        width: u32,
+        height: u32,
+    ) -> Self {
+        let make = |label| {
+            device.create_texture(&wgpu::TextureDescriptor {
+                label: Some(label),
+                size: wgpu::Extent3d {
+                    width,
+                    height,
+                    depth_or_array_layers: 1,
+                },
+                mip_level_count: 1,
+                sample_count: 1,
+                dimension: wgpu::TextureDimension::D2,
+                format: DATA_FORMAT,
+                usage: wgpu::TextureUsages::RENDER_ATTACHMENT
+                    | wgpu::TextureUsages::TEXTURE_BINDING,
+                view_formats: &[],
+            })
+        };
+        let textures = [
+            make("DE distance seeds A"),
+            make("DE distance seeds B"),
+            make("DE distance field"),
+        ];
+        let views = textures
+            .each_ref()
+            .map(|t| t.create_view(&wgpu::TextureViewDescriptor::default()));
+        let inputs = [
+            lp.bind_group(device, data, &views[0]),
+            lp.bind_group(device, data, &views[1]),
+        ];
+        Self {
+            textures,
+            views,
+            inputs,
+            slots: lipschitz_slots(width, height),
+        }
+    }
+
+    /// The data texture with the rebuilt DE.
+    fn output(&self) -> &wgpu::TextureView {
+        &self.views[2]
+    }
+
+    /// Record seed → jump passes → compose into [`Self::output`].
+    fn record(&self, encoder: &mut wgpu::CommandEncoder, lp: &Lipschitz) {
+        let pass = |encoder: &mut wgpu::CommandEncoder,
+                    target: &wgpu::TextureView,
+                    pipeline: &wgpu::RenderPipeline,
+                    input: &wgpu::BindGroup,
+                    slot: u32| {
+            let mut pass = encoder.begin_render_pass(&wgpu::RenderPassDescriptor {
+                label: Some("lipschitz pass"),
+                color_attachments: &[Some(wgpu::RenderPassColorAttachment {
+                    view: target,
+                    depth_slice: None,
+                    resolve_target: None,
+                    ops: wgpu::Operations {
+                        load: wgpu::LoadOp::Clear(wgpu::Color::BLACK),
+                        store: wgpu::StoreOp::Store,
+                    },
+                })],
+                depth_stencil_attachment: None,
+                timestamp_writes: None,
+                occlusion_query_set: None,
+                multiview_mask: None,
+            });
+            pass.set_pipeline(pipeline);
+            pass.set_bind_group(0, input, &[slot * LIPSCHITZ_STRIDE]);
+            pass.draw(0..3, 0..1);
+        };
+        // Seeds into A (the bound seed texture, B, is unread).
+        pass(encoder, &self.views[0], &lp.seed, &self.inputs[1], 0);
+        // Pass i reads seeds i % 2 and writes the other.
+        for (i, &slot) in self.slots.iter().enumerate() {
+            pass(encoder, &self.views[(i + 1) % 2], &lp.jump, &self.inputs[i % 2], slot);
+        }
+        let last = self.slots.len() % 2;
+        pass(encoder, &self.views[2], &lp.compose, &self.inputs[last], 0);
+    }
+}
+
+/// Jump-flooding step slots (step = 2^slot) for a `width`×`height` texture:
+/// from about half its larger side down to 1, then one more step-1 pass,
+/// which fixes most of jump flooding's residual errors.
+fn lipschitz_slots(width: u32, height: u32) -> Vec<u32> {
+    let top = (width.max(height) / 2).max(1).ilog2();
+    (0..=top).rev().chain(std::iter::once(0)).collect()
+}
+
 /// The interactive iteration pipelines for one [`PipelineKey`].
 struct IteratePipelines {
     /// 1-spp perturbation iterate → data texture (`fs_data`).
@@ -253,6 +489,10 @@ struct CacheTarget {
     /// Refine pass output + the colourise bind group reading it. Only
     /// allocated while AA is on: it's a second full-size `Rgba32Float`.
     aa: Option<(wgpu::TextureView, wgpu::BindGroup)>,
+    /// The distance-field rebuild of the refined (or 1-spp) data + the
+    /// colourise bind group reading it. Allocated on first use, only for
+    /// shadow / 3D Complex Multibrot (see [`wants_envelope`]).
+    envelope: Option<(Envelope, wgpu::BindGroup)>,
     /// Blit pass input: the colour texture + sampler.
     blit_bind_group: wgpu::BindGroup,
     width: u32,
@@ -302,6 +542,12 @@ pub struct FractalRenderer {
     /// Colourise pass: data texture → colour texture (palette mapping).
     colorize_pipeline: wgpu::RenderPipeline,
     colorize_bind_group_layout: wgpu::BindGroupLayout,
+    /// Distance-field passes for shadow / 3D Complex Multibrot (see
+    /// [`wants_envelope`]).
+    lipschitz: Lipschitz,
+    /// Whether the cache's envelope matches the current data texture. Not
+    /// implied by iteration: switching shadow → 3D doesn't re-iterate.
+    envelope_valid: bool,
 
     /// Blit pipeline + resources that copy the colour texture to egui's surface.
     blit_pipeline: wgpu::RenderPipeline,
@@ -633,6 +879,8 @@ impl FractalRenderer {
             uploaded_lights: None,
             colorize_pipeline,
             colorize_bind_group_layout,
+            lipschitz: Lipschitz::new(device),
+            envelope_valid: false,
             blit_pipeline,
             blit_bind_group_layout,
             blit_sampler,
@@ -662,7 +910,8 @@ impl FractalRenderer {
         // Any commands using them were submitted on earlier frames, and
         // `destroy()` defers the actual free until those finish.
         if let Some(old) = self.cache.take() {
-            for t in &old.textures {
+            let envelope = old.envelope.iter().flat_map(|e| &e.0.textures);
+            for t in old.textures.iter().chain(envelope) {
                 t.destroy();
             }
         }
@@ -715,24 +964,13 @@ impl FractalRenderer {
         let color_view = color_texture.create_view(&wgpu::TextureViewDescriptor::default());
 
         let colorize_bind_group_for = |data: &wgpu::TextureView| {
-            device.create_bind_group(&wgpu::BindGroupDescriptor {
-                label: Some("colorize bind group"),
-                layout: &self.colorize_bind_group_layout,
-                entries: &[
-                    wgpu::BindGroupEntry {
-                        binding: 0,
-                        resource: self.uniform_buffer.as_entire_binding(),
-                    },
-                    wgpu::BindGroupEntry {
-                        binding: 1,
-                        resource: wgpu::BindingResource::TextureView(data),
-                    },
-                    wgpu::BindGroupEntry {
-                        binding: 2,
-                        resource: self.lights_buffer.as_entire_binding(),
-                    },
-                ],
-            })
+            colorize_bind_group(
+                device,
+                &self.colorize_bind_group_layout,
+                &self.uniform_buffer,
+                &self.lights_buffer,
+                data,
+            )
         };
         let colorize_bind_group = colorize_bind_group_for(&data_view);
         let aa_target = data_aa_texture.as_ref().map(|t| {
@@ -775,6 +1013,7 @@ impl FractalRenderer {
             refine_bind_group,
             colorize_bind_group,
             aa: aa_target,
+            envelope: None,
             blit_bind_group,
             width,
             height,
@@ -818,7 +1057,8 @@ impl FractalRenderer {
     /// lock on the renderer), its bind-group layout, and the target format.
     /// In 3D mode (`rendering_mode == 2`) also the interactive iterate →
     /// refine → colourise chain, since the raymarcher needs a whole data
-    /// texture to march over and `fs_color` has no 3D path.
+    /// texture to march over and `fs_color` has no 3D path. Likewise for
+    /// the distance field ([`wants_envelope`]), which needs the whole image.
     pub fn export_handles(&self, device: &wgpu::Device, uniforms: &Uniforms) -> ExportHandles {
         let constants = PipelineKey::from_uniforms(uniforms).constants();
         let pipeline = fullscreen_pipeline(
@@ -830,7 +1070,8 @@ impl FractalRenderer {
             self.target_format,
             &constants,
         );
-        let raymarch = (uniforms.rendering_mode == 2).then(|| RaymarchHandles {
+        let chain = uniforms.rendering_mode == 2 || wants_envelope(uniforms);
+        let raymarch = chain.then(|| RaymarchHandles {
             iterate: fullscreen_pipeline(
                 device,
                 "fractal export iterate pipeline",
@@ -852,6 +1093,7 @@ impl FractalRenderer {
             colorize: self.colorize_pipeline.clone(),
             refine_bind_group_layout: self.refine_bind_group_layout.clone(),
             colorize_bind_group_layout: self.colorize_bind_group_layout.clone(),
+            lipschitz: wants_envelope(uniforms).then(|| self.lipschitz.clone()),
         });
         ExportHandles {
             pipeline,
@@ -870,11 +1112,11 @@ pub struct ExportHandles {
     pipeline: wgpu::RenderPipeline,
     bind_group_layout: wgpu::BindGroupLayout,
     format: wgpu::TextureFormat,
-    /// The two-pass chain, for 3D mode only.
+    /// The two-pass chain, for 3D mode and the distance field only.
     raymarch: Option<RaymarchHandles>,
 }
 
-/// The interactive two-pass pipelines, for a 3D export.
+/// The interactive two-pass pipelines, for a 3D or distance-field export.
 #[derive(Clone)]
 struct RaymarchHandles {
     iterate: wgpu::RenderPipeline,
@@ -882,15 +1124,19 @@ struct RaymarchHandles {
     colorize: wgpu::RenderPipeline,
     refine_bind_group_layout: wgpu::BindGroupLayout,
     colorize_bind_group_layout: wgpu::BindGroupLayout,
+    /// The distance-field passes, when [`wants_envelope`].
+    lipschitz: Option<Lipschitz>,
 }
 
-/// A 3D export's own data textures and the passes that fill them: the tiles
-/// iterate into `data_view`, then one refine (if AA) + colourise pass
-/// raymarches the finished height field into the export target.
+/// A 3D (or distance-field shadow) export's own data textures and the passes
+/// that fill them: the tiles iterate into `data_view`, then one refine (if
+/// AA), the distance-field rebuild (if wanted) and a colourise pass render
+/// the finished height field into the export target.
 struct RaymarchExport {
     iterate: wgpu::RenderPipeline,
     /// Refine pipeline, output view and input bind group, when AA is on.
     refine: Option<(wgpu::RenderPipeline, wgpu::TextureView, wgpu::BindGroup)>,
+    envelope: Option<(Lipschitz, Envelope)>,
     colorize: wgpu::RenderPipeline,
     colorize_bind_group: wgpu::BindGroup,
     data_view: wgpu::TextureView,
@@ -914,7 +1160,8 @@ pub struct ExportRender {
     /// Number of horizontal tiles the render is split into.
     pub tiles: u32,
     pub swap_rb: bool,
-    /// 3D mode: tiles fill a data texture instead of the target.
+    /// 3D mode or the distance field: tiles fill a data texture instead of
+    /// the target.
     raymarch: Option<RaymarchExport>,
 }
 
@@ -1066,29 +1313,25 @@ impl ExportRender {
                     refine_bind_group,
                 )
             });
-            // Colourise reads the refined texture when AA is on.
-            let colorize_input = refine.as_ref().map_or(&data_view, |(_, v, _)| v);
-            let colorize_bind_group = device.create_bind_group(&wgpu::BindGroupDescriptor {
-                label: Some("export colorize bind group"),
-                layout: &rm.colorize_bind_group_layout,
-                entries: &[
-                    wgpu::BindGroupEntry {
-                        binding: 0,
-                        resource: uniform_buffer.as_entire_binding(),
-                    },
-                    wgpu::BindGroupEntry {
-                        binding: 1,
-                        resource: wgpu::BindingResource::TextureView(colorize_input),
-                    },
-                    wgpu::BindGroupEntry {
-                        binding: 2,
-                        resource: lights_buffer.as_entire_binding(),
-                    },
-                ],
+            // The distance field reads the refined texture when AA is on,
+            // and colourise reads the distance field, else the same texture.
+            let refined = refine.as_ref().map_or(&data_view, |(_, v, _)| v);
+            let envelope = rm.lipschitz.as_ref().map(|lp| {
+                let env = Envelope::new(device, lp, refined, width, height);
+                (lp.clone(), env)
             });
+            let colorize_input = envelope.as_ref().map_or(refined, |(_, e)| e.output());
+            let colorize_bind_group = colorize_bind_group(
+                device,
+                &rm.colorize_bind_group_layout,
+                &uniform_buffer,
+                &lights_buffer,
+                colorize_input,
+            );
             RaymarchExport {
                 iterate: rm.iterate.clone(),
                 refine,
+                envelope,
                 colorize: rm.colorize.clone(),
                 colorize_bind_group,
                 data_view,
@@ -1120,8 +1363,9 @@ impl ExportRender {
 
     /// Render one horizontal tile into the export texture and submit it. Tile 0
     /// clears the whole attachment; later tiles preserve earlier ones. In 3D
-    /// mode the tiles iterate into the data texture instead, and the last one
-    /// also runs the (whole-image) refine + raymarching colourise passes.
+    /// mode (or with the distance field) the tiles iterate into the data
+    /// texture instead, and the last one also runs the whole-image refine,
+    /// distance-field and colourise passes.
     pub fn render_tile(&self, device: &wgpu::Device, queue: &wgpu::Queue, t: u32) {
         let (y0, y1) = self.tile_rows(t);
         if y1 <= y0 {
@@ -1176,6 +1420,9 @@ impl ExportRender {
                     &[&self.bind_group, refine_bind_group],
                 );
             }
+            if let Some((lp, env)) = &rm.envelope {
+                env.record(&mut encoder, lp);
+            }
             data_pass(
                 &mut encoder,
                 "export colorize pass",
@@ -1399,6 +1646,35 @@ pub fn encode_png_with_progress(
     out
 }
 
+/// Colourise pass input: the uniforms, the data texture `data` to colour and
+/// the lights.
+fn colorize_bind_group(
+    device: &wgpu::Device,
+    layout: &wgpu::BindGroupLayout,
+    uniforms: &wgpu::Buffer,
+    lights: &wgpu::Buffer,
+    data: &wgpu::TextureView,
+) -> wgpu::BindGroup {
+    device.create_bind_group(&wgpu::BindGroupDescriptor {
+        label: Some("colorize bind group"),
+        layout,
+        entries: &[
+            wgpu::BindGroupEntry {
+                binding: 0,
+                resource: uniforms.as_entire_binding(),
+            },
+            wgpu::BindGroupEntry {
+                binding: 1,
+                resource: wgpu::BindingResource::TextureView(data),
+            },
+            wgpu::BindGroupEntry {
+                binding: 2,
+                resource: lights.as_entire_binding(),
+            },
+        ],
+    })
+}
+
 /// Record one fullscreen-triangle pass drawing `pipeline` into `target`
 /// (cleared first), with `bind_groups` bound to groups 0, 1, ...
 fn data_pass(
@@ -1534,6 +1810,25 @@ impl egui_wgpu::CallbackTrait for FractalCallback {
         if iter_dirty {
             renderer.ensure_pipelines(device, PipelineKey::from_uniforms(&self.uniforms));
         }
+        let envelope = wants_envelope(&self.uniforms);
+        if envelope
+            && let Some(cache) = &renderer.cache
+            && cache.envelope.is_none()
+        {
+            let src = cache.aa.as_ref().map_or(&cache.data_view, |(v, _)| v);
+            let env = Envelope::new(device, &renderer.lipschitz, src, cache.width, cache.height);
+            let bind_group = colorize_bind_group(
+                device,
+                &renderer.colorize_bind_group_layout,
+                &renderer.uniform_buffer,
+                &renderer.lights_buffer,
+                env.output(),
+            );
+            if let Some(cache) = &mut renderer.cache {
+                cache.envelope = Some((env, bind_group));
+            }
+        }
+        let mut envelope_ran = false;
         let pipelines = &renderer.pipelines[&PipelineKey::from_uniforms(&self.uniforms)];
         if let Some(cache) = &renderer.cache {
             if iter_dirty {
@@ -1557,11 +1852,23 @@ impl egui_wgpu::CallbackTrait for FractalCallback {
                 }
             }
 
+            // Shadow / 3D Complex Multibrot: rebuild the DE as a distance field.
+            let env = cache.envelope.as_ref().filter(|_| envelope);
+            if let Some((env, _)) = env
+                && (iter_dirty || !renderer.envelope_valid)
+            {
+                env.record(egui_encoder, &renderer.lipschitz);
+                envelope_ran = true;
+            }
+
             // Colourise pass: data texture → colour texture.
-            let colorize_bind_group = cache
+            let colorize_bind_group = match env {
+                Some((_, bg)) => bg,
+                None => cache
                     .aa
                     .as_ref()
-                .map_or(&cache.colorize_bind_group, |(_, bg)| bg);
+                    .map_or(&cache.colorize_bind_group, |(_, bg)| bg),
+            };
             data_pass(
                 egui_encoder,
                 "fractal colorize pass",
@@ -1571,6 +1878,7 @@ impl egui_wgpu::CallbackTrait for FractalCallback {
             );
         }
 
+        renderer.envelope_valid = envelope_ran || (renderer.envelope_valid && !iter_dirty);
         if iter_dirty {
             renderer.iterated = Some(IterState {
                 uniforms: self.uniforms,

src/shaders/lipschitz.wgsl

@@ -0,0 +1,121 @@
+// Distance field for the shadow and 3D views of kinds whose map is
+// discontinuous (Complex Multibrot's principal-branch z^p). The per-pixel
+// DE, |z|·ln|z|/|dz| = G/|G'|, is only a distance when the potential G is
+// continuous. Across a branch-cut preimage G jumps (|z| jumps by
+// e^(2π·Im p)), each side's DE describes the set as continued on its own
+// branch: seams in shadow mode, walls in the raymarched terrain. A true
+// distance to the set is continuous, so this rebuilds one from the pixels that are unambiguously
+// next to the set ("seeds": interior texels, and exterior texels whose DE is
+// below SEED_DE, i.e. within about a pixel of it):
+//     h(x) = min over seeds y of  DE(y) + DIST_SLOPE·|x - y|
+// computed by jump flooding: `fs_seed` marks seeds, `fs_jump` runs with
+// `step` halving from about half the texture size down to 1 (plus one more
+// step-1 pass), each texel keeping the best seed among itself and its 8
+// neighbours at ±step, and `fs_compose` writes the result, eased by
+// `ease_distance`, as the data texture's G channel. Seeds are carried as coordinates, so the distance is
+// Euclidean rather than an 8-direction chamfer approximation.
+//
+// The set only counts where it's in view: next to the image edge, set just
+// outside it is missed and the height there reads a bit high.
+//
+// Texel layout of the seed textures: (seed x, seed y, seed DE, 1), or all 0
+// for "no seed yet". R (palette parameter) and B (interior fraction) of the
+// data texture pass through untouched.
+
+struct LipschitzStep {
+    step: i32,
+    _pad0: i32,
+    _pad1: i32,
+    _pad2: i32,
+};
+
+@group(0) @binding(0) var data_tex: texture_2d<f32>;
+@group(0) @binding(1) var seed_tex: texture_2d<f32>;
+@group(0) @binding(2) var<uniform> ls: LipschitzStep;
+
+// DE units per texel of a true distance: DE is in units of `pixel_size`,
+// the texel's (|dx| + |dy|) footprint, i.e. sqrt(2) texels.
+const DIST_SLOPE: f32 = 0.70710678;
+// Exterior texels with a DE below this (in DE units) are seeds.
+const SEED_DE: f32 = 1.0;
+
+@vertex
+fn vs_main(@builtin(vertex_index) idx: u32) -> @builtin(position) vec4<f32> {
+    return vec4<f32>(fullscreen_triangle_pos(idx), 0.0, 1.0);
+}
+
+@fragment
+fn fs_seed(@builtin(position) pos: vec4<f32>) -> @location(0) vec4<f32> {
+    let p = vec2<i32>(pos.xy);
+    let d = textureLoad(data_tex, p, 0);
+    if d.b != 0.0 {
+        return vec4<f32>(vec2<f32>(p), 0.0, 1.0);
+    }
+    if d.g < SEED_DE {
+        return vec4<f32>(vec2<f32>(p), d.g, 1.0);
+    }
+    return vec4<f32>(0.0);
+}
+
+// Height at `p` through seed `s` (a seed texel), or +inf for "no seed".
+fn through(p: vec2<i32>, s: vec4<f32>) -> f32 {
+    if s.a == 0.0 {
+        return 3.0e38;
+    }
+    return s.z + DIST_SLOPE * distance(vec2<f32>(p), s.xy);
+}
+
+@fragment
+fn fs_jump(@builtin(position) pos: vec4<f32>) -> @location(0) vec4<f32> {
+    let p = vec2<i32>(pos.xy);
+    let hi = vec2<i32>(textureDimensions(seed_tex)) - vec2<i32>(1, 1);
+    let st = ls.step;
+    var best = textureLoad(seed_tex, p, 0);
+    var best_h = through(p, best);
+    for (var dy = -1; dy <= 1; dy++) {
+        for (var dx = -1; dx <= 1; dx++) {
+            if dx == 0 && dy == 0 {
+                continue;
+            }
+            let q = p + st * vec2<i32>(dx, dy);
+            if any(q < vec2<i32>(0, 0)) || any(q > hi) {
+                continue;
+            }
+            let s = textureLoad(seed_tex, q, 0);
+            let h = through(p, s);
+            if h < best_h {
+                best = s;
+                best_h = h;
+            }
+        }
+    }
+    return best;
+}
+
+// Scale of `ease_distance`, in screen heights.
+const EASE_K: f32 = 0.02;
+
+// Concave easing of the distance field `h` (DE units, `size_y` texels
+// tall): K·ln(1 + x/K) in screen heights, the unit `sdf` in colorize.wgsl
+// reads. Slope 1 at the set, flattening far from it, so the terrain rises
+// steeply out of the set and then levels off. The slope never exceeds 1,
+// so the field stays a valid (conservative) distance for the sphere tracer.
+fn ease_distance(h: f32, size_y: f32) -> f32 {
+    return EASE_K * log(1.0 + h / (size_y * EASE_K)) * size_y;
+}
+
+@fragment
+fn fs_compose(@builtin(position) pos: vec4<f32>) -> @location(0) vec4<f32> {
+    let p = vec2<i32>(pos.xy);
+    let d = textureLoad(data_tex, p, 0);
+    if d.b != 0.0 {
+        return d;
+    }
+    // Not min(h, DE): that keeps the too-low side of every jump, so the
+    // walls come back as shards.
+    let h = through(p, textureLoad(seed_tex, p, 0));
+    if h >= 3.0e38 {
+        return d; // no set anywhere in view: keep the DE
+    }
+    return vec4<f32>(d.r, ease_distance(h, f32(textureDimensions(data_tex).y)), d.b, d.a);
+}

tests/shader_valid.rs

@@ -122,6 +122,17 @@ fn colorize_shader_is_valid() {
     );
 }
 
+#[test]
+fn lipschitz_shader_is_valid() {
+    validate(
+        "lipschitz.wgsl",
+        concat!(
+            include_str!("../src/shaders/common.wgsl"),
+            include_str!("../src/shaders/lipschitz.wgsl"),
+        ),
+    );
+}
+
 #[test]
 fn blit_shader_is_valid() {
     validate(